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Rate of convergence of depth contours: with application to a multivariate metrically trimmed mean

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  • Kim, Jeankyung

Abstract

In a recent paper of He and Wang (1997, Ann. Statist. 25, 495-504), they considered depth contours based on data depth and they proved a uniform contour convergence theorem under some conditions on the depth measure. In this paper we prove n-1/2 rate of convergence of depth contours using empirical process and U-process theory. This result is then applied to get n-1/2 rate of convergence of a multivariate metrically trimmed mean.

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  • Kim, Jeankyung, 2000. "Rate of convergence of depth contours: with application to a multivariate metrically trimmed mean," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 393-400, October.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:4:p:393-400
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    References listed on IDEAS

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    1. Nolan, D., 1992. "Asymptotics for multivariate trimming," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 157-169, August.
    2. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
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    Cited by:

    1. Hwang, Jinsoo & Jorn, Hongsuk & Kim, Jeankyung, 2004. "On the performance of bivariate robust location estimators under contamination," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 587-601, January.
    2. Petra Laketa & Stanislav Nagy, 2022. "Halfspace depth for general measures: the ray basis theorem and its consequences," Statistical Papers, Springer, vol. 63(3), pages 849-883, June.
    3. Kim, Jeankyung & Hwang, Jinsoo, 2001. "Asymptotic properties of location estimators based on projection depth," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 293-299, December.
    4. Burr, Michael A. & Fabrizio, Robert J., 2017. "Uniform convergence rates for halfspace depth," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 33-40.
    5. Olive, David J., 2004. "A resistant estimator of multivariate location and dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 93-102, May.

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